And the Sox are tied for dead last amongst the charter teams in WS appearances along with Cleveland.

Yes, but they are tied with the Orioles/Browns (the franchise of Tito Landrum and double the World Series appearance of the White Sox) for World Series titles. They also are tied with the Senators/Twins for World Series titles. The Tigers only have four and the Indians only have two.

It didn't help the White Sox that they had of their best teams during the second golden age of the Yankees.